Cosmological Bounds on the Generalized Uncertainty Principle from the CMB

Abstract

We constrain the deformation parameter $β$ of the Generalized Uncertainty Principle with cosmological observations. A quadratic deformation of the Heisenberg uncertainty principle modifies the Friedmann equations of $Λ$CDM and gives rise to a phenomenological dynamical dark energy with a single free parameter, $β$. To avoid a singular behaviour for the effective dark energy equation of state parameter, we restrict the prior to non-negative values of $β$. Using Planck 2018 CMB temperature and polarization data together with DESI DR2 BAO and Pantheon+SH0ES supernovae, we find the upper limit $β<0.00728~$ at $68\%$ confidence interval. The resulting cosmological model fits the data slightly better than $Λ$CDM, providing smaller value for the $χ_{min}^{2}% $, such that the Akaike Information Criterion to suggest statistical equivalency between the two models, although the Bayesian evidence favours the $Λ$CDM. Finally, the quadratic Generalized Uncertainty Principle does not alleviate the $H_{0}$ tension, it reduces the tension to $4.8σ$, that is, due to the small correlation between the $H_{0}-β$ parameters.